converting polar to rectangular calculator

What this calculator does

This converter changes a point from polar form (r, θ) into rectangular (Cartesian) form (x, y). It works for both degrees and radians and is useful for trigonometry, precalculus, physics, engineering, and complex numbers.

Polar to rectangular formula

To convert from polar coordinates (r, θ) to rectangular coordinates (x, y), use:

• x = r cos(θ)
• y = r sin(θ)

If your angle is in degrees, convert to radians first for many programming tools: θrad = θdeg × π / 180.

How to use the calculator

1. Enter the radius r.
2. Enter the angle θ.
3. Choose whether the angle is in degrees or radians.
4. Set how many decimal places you want.
5. Click Convert to Rectangular.

Worked examples

Example 1: (r = 5, θ = 53.13°)

x = 5 cos(53.13°) ≈ 3
y = 5 sin(53.13°) ≈ 4
So the rectangular point is approximately (3, 4).

Example 2: (r = 10, θ = π/6)

In radians: cos(π/6)=√3/2, sin(π/6)=1/2
x = 10(√3/2) ≈ 8.6603
y = 10(1/2) = 5
Rectangular form: (8.6603, 5).

Common mistakes to avoid

• Using degrees when your calculator expects radians.
• Forgetting that negative angles are valid.
• Rounding too early during intermediate steps.
• Mixing up sine and cosine in the formulas.

Why this conversion matters

Polar coordinates are natural for circular motion and direction-based data. Rectangular coordinates are often easier for graphing and algebraic operations. Converting between the two gives you flexibility and helps you solve geometry and complex-number problems faster.

Quick reference

• Input: (r, θ)
• Output: (x, y)
• Core formulas: x = r cos θ, y = r sin θ
• Complex number form: z = x + yi